If the volume of n moles of a monatomic perfect gas with an initial
volume V and an initial temperature T is halved at a constant rate while
its temperature is doubled at a constant rate, how can I prove that the
work done to the gas is given by W = nRT*(3*log[2]-1)?

A 15-gram bullet strikes and becomes embedded in a 1.10 kg block of wood
placed on a horizontal surface just in front of the gun. If the
coefficient of friction between the block and the surface is .25 and the
impact drives the block 9.5 meters before it comes to rest, what was the
muzzle speed of the bullet?

When a car accelerates, what forces are involved? I'm curious both
about the car itself and the forces experienced by a person sitting in
the car as they are pushed back against the seat with acceleration and
pushed against their seat belt when the car slows. What's going on
there in terms of physics?

Newton's third law says that when you exert a force on an object, the
object exerts an equal and opposite force back on you. If that's true,
how can I push something and have it move? Wouldn't the forces cancel
out and the object stay at rest?

Consider a balloon filled with helium, hanging from the floor of a
car. The car is sealed, and is full of air at ambient surface
pressure. If the car undergoes constant acceleration forwards only,
which way, relative to the car, will the balloon move?

How can I find out when a plane, whose position approaching an airport is
described parametrically by P_t = (1000,500,900)+ t[-100,-50,-90], will
be closest to the traffic control center, located at (24,11,13)?

A particle is projected with initial velocity v and angle theta in a
parabolic path. How can I show that at time t, when the angle to the
horizontal is gamma, tan(gamma) = tan(theta) - (gt/v) sec(theta)?

The half-life of a radioactive element is 131 days, but your sample
will not be useful to you after 90% of the radioactive nuclei
originally present have disintegrated. For about how many days can you
use the sample?